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\begin{document}
\title{Lab 1: Flicker Photometry}
\author{Alexandra Booth \and Glenn Sweeney}

% make the title area
\maketitle

% make introduction
\section{Introduction}

In this lab, we examined temporal mixing with the human visual system. 
Temporal mixing is the phenomenon that describes the visual merging of different stimuli when they are presented to a region of the visual system in quick succession. 
Interestingly, complete temporal mixing occurs at different frequencies for color perception and brightness perception.
If two samples are presented at approximately 60Hz (which means the pair is cycled 60 times per second), then both their brightness and their color merge together.
At and above these frequencies, the cycling is virtually undetectable in the fovea of the human visual system.

However, if this frequency is decreased, the visual brightness of the two patches will begin to become distinct. Depending on the difference between the two patches, the sample area may begin to flicker.
However, between 30Hz and 60Hz, an interesting visual phenomenon occurs.
The brightness difference appears as a flicker, but the human color response does not yet distinguish the difference between the two colors, and percieves only the blend of the two samples.
Using this phenomenon, a frequency may be selected in this range in order to separate the visual appearance of lightness from the visual appearance of hue and saturation.
Then, an observer can compare and adjust the relative perceptual brightness of two samples without an influence from the color of the patches.
This can help match brightness for colors that are normally difficult to compare, such as reds and greens.


\section{Procedure}

In this lab we use this technique, called flicker photometry, to compare the brightness of samples with different hues and saturations.
In each trial, a chromatic color sample is mixed with a reference neutral.
The brightness of the neutral is user adjustable.
These samples were cycled in the same spatial location at approximately 40Hz.
By adjusting the brightness of the reference patch until the brightness flicker was removed, a visually matched brightness level could be measured.
Then, each sample was measured with an illuminance meter.
These results were compared to see how effective the flicker photometry method was to quantify the percieved brightness for the human visual system.

In order to compare the collected data to the actual brightness of each patch, the luminance of each was measured.
To collect this measurement, a Minolta illuminance meter was used.
This tool measures the incident illuminance at the plane of the device's sensor.
It is also equipped with a hemispherical integrating dome to calculate incident radiation from a large area.
In order to collect luminance information with this device, several pieces of information need to be known.
The calculation from illuminance to luminance requires information about the solid angle being considered.
Also, because we are interested in exitant luminance, the size of the detector as well as the size of the radiating sample would need to be known.
Finally, the distance from the sensor to the area would need to be known.
Given the geometry of our problem, this computation is very complex.
A large area source was used at a relatively near distance, the source was a difficult shape to calculate solid angle for, the behavior of the detector dome is unknown, and no tools were provided to measure distances with adequate precision. 
However, an attempt was made to keep all of these unknown terms constant during measurement.
As a result, the only varying term is the amount of flux output by the patch.
Because of this, the illuminances measured in this experiment are considered to be proportional to the exitant luminance of each patch.
\FloatBarrier

\section{Results}

Table \ref{tbl:Yvalues} contains the Y values for each true patch, as well as the Y value obtained in the experiment by each observer.
It is these values that can be seen in the plot of figure \ref{fig:Ycomp}.
It can be seen that the general trend of increasing lrightness was found. However, at low lightness, both observers over-estimated the lightness, while for ligher batches both observers consistently under-estimated.
One observer constistenly estimated a higher lightness than the other.
The reasons for this are unknown.

Next, the Y values for every patch in this experiment were plotted against the relative luminance values measured.
The resultant plot can be seen in figure \ref{fig:LversusY}.
The plot demonstrates a trend in the relative luminance versus the Y value.
As relative luminance increases the Y value increases.
However, there is no apparent trend when looking at the $x$ or $y$ value plotted against the luminance (Figure \ref{fig:Lversusxy}).
This means that it is the Y componant that best represents luminance.
Note that there appear to be horizontal lines at $y=0.35$ and $x=0.3$.
These are present because a large number of patches measured were neutral, and thus had the same x-y chromaticity.
For a more uniform sample set, this correlation would most likely disappear.

\begin{table}
\caption{Actual and Observer Y values for each sample.}
\label{tbl:Yvalues}
\centering
\begin{tabular}{|c|c|c|c|}
\hline
 \multicolumn{4}{|c|}{Y Values} \\ \hline
Sample	&	Actual	&	Observer 1	&	Observer 2	\\ \hline
a	&	50.008	&	46	&	50.5	\\ \hline
b	&	73.393	&	49.5	&	62.5	\\ \hline
c	&	11.53	&	10.5	&	10.5	\\ \hline
d	&	33.937	&	36	&	42	\\ \hline
e	&	9.131	&	9	&	10.5	\\ \hline

\end{tabular}
\end{table}

\begin{table}
\caption{xy chromaticity values for each of the patches, including the neutral patch used in the experiment. The observed color for each set of coordinates is also included.}
\label{tbl:xyvalues}
\centering
\begin{tabular}{|c|c|c|c|}
\hline
 \multicolumn{4}{|c|}{$xy$ chromaticities for each patch} \\ \hline
Sample	&	x	&	y	&	Color	\\ \hline
a	&	0.458	&	0.453	&	orange	\\ \hline
b	&	0.308	&	0.453	&	green	\\ \hline
c	&	0.252	&	0.365	&	teal	\\ \hline
d	&	0.253	&	0.215	&	lavender	\\ \hline
e	&	0.166	&	0.081	&	violet	\\ \hline
neutral	&	0.3065	&	0.3468	&	grey	\\ \hline
\end{tabular}
\end{table}

\begin{figure}
\centering
\includegraphics[width=0.6\textwidth]{Yvalue_comp.eps}
\caption{Plot of the colored patches actual Y value and the Y values obtained by each observer in the experiment.}
\label{fig:Ycomp}
\end{figure}


\begin{figure}
\centering
\includegraphics[width=0.6\textwidth]{L_versus_Y.eps}
\caption{Luminance value of each sample versus the Y value.}
\label{fig:LversusY}
\end{figure}

\begin{figure}
\centering
\includegraphics[width=0.6\textwidth]{L_versus_xy.eps}
\caption{The luminance value of each sample versus the $xy$ chromaticity values.}
\label{fig:Lversusxy}
\end{figure}

\FloatBarrier

\section{Analysis and Conclusions}

As expected, a high positive correlation between relative luminance and Y was found.
This supports the observation that Y is an approximate metric of brightness.
However, it is important to note that while both Y and relative luminance correspond directly to the human's perception of brightness, neither scales linearly with percieved brightness.

Some considerable sources of error existed in this lab.
The flicker photometry experiment was carried out on an LCD monitor with a 60Hz refresh rate.
As a result, it was impossible to refresh the two samples at exactly 40Hz.
Instead, signficiant "tearing" was created because the 40Hz refresh frequency aliased with the monitor's refresh rate.
This made it difficult to match some colors effectively.
To overcome this error, the experimenters attempted to place the visual field in the periphery of the human visual system.
In the far periphery, the human sensititivy to flicker decreases.
Thus, the necessary refresh rate for the visual system dropped to match the actual refresh rate being generated with the monitor, and the expected flicker was more satisfactorily viewable.

Also, the illuminance meter supplied was not the optimal tool to measure each color patch as displayed on the screen.
The illuminance meter measured the incident illuminance at the detector plane, as captured from a hemispherical viewing area.
The exact angular sensitivity was not provided, but it is clear from the geometry of the device that it was sensitive through a very large solid angle.
Because of this, many factors contributed to the final illuminace reading, including reflections in the room and graphical elements on the monitor. As a result, calculating the actual relative illuminance between displayed patches becomes difficult.
Also the illuminance meter is sensitive to the distance from the sensor to the patch and the size of the patch, neither of which could be controlled well in the experimental setup. As a result, considerable error exists in the luminance measurements.

Overall, although this lab provided an approximation of flicker photometry, the lack of proper display and measurement tools made it difficult to conduct the experiment properly.
Even so, we were able to observe basic trends in the data that were similar to the expected relationships.


\end{document}
